For definiteness, we will work with \(c_B^{\rm dec} \simeq 0.05\)  in the following.
We, however, caution that this estimate comes with a considerable numerical uncertainty of up to three orders of magnitude.
On the one hand, the ratio \(H/\Gamma _{\rm ws}\)  is exponentially sensitive to the chosen freeze-out temperature, simply because \(\Gamma _{\rm ws}\)  decreases exponentially fast during the EWPT [see Eq. (REF )].
On the other hand, the accuracy of the one-loop result in Eq. (REF ) is limited, which is, e.g., reflected in the fact that it only roughly agrees with the numerical lattice results in Ref. [1]} (for more details, see also the discussion in Refs. [2]}, [3]}).
A more accurate determination of the temperature dependence of the weak mixing angle during the EWPT is, however, not available at present, which is why we will content ourselves with \(c_B^{\rm dec} \simeq 0.05\)  as a representative benchmark value in our analysis.
